Fifa's secretary general has been forced to deny claims that he attempted to persuade the presidential challenger Mohamed bin Hammam to withdraw from the race, as the world governing body faced another flurry of corruption allegations. German broadcasters claimed on Monday that Jérôme Valcke, who is overseeing the election campaign, put pressure on Bin Hammam to withdraw.

"Contrary to some media allegations I want to make it very clear that neither I nor anyone else at Fifa have asked Mr Mohammed bin Hammam at any point to withdraw his candidature for the upcoming Fifa presidency election," said Valcke, whose position could be under threat if Bin Hammam were to defeat Blatter in the 1 June election. "The last time I met the AFC [Asian Football Confederation] president was at the Conmebol Congress in Asunción on 1 May, where we simply greeted each other. Again these allegations are totally untrue."

The Football Association has promised that an independent review by James Dingemans QC of claims made under parliamentary privilege by its former chairman Lord Triesman will be finished by Friday. Triesman claimed four members of the Fifa executive committee – Jack Warner, Ricardo Teixeira, Nicolas Leoz and Worawi Makudi – had sought bribes or inducements during the 2018 World Cup bid campaign. They have denied the allegations.

Qatari 2022 bid officials on Monday denounced separate bribery claims and sought to discredit an "embittered" whistleblowing former employee who is set to give evidence to Fifa on Wednesday. They said there was no evidence to support the claims, made by the Sunday Times to a parliamentary committee, that two Fifa executive committee members had been offered $1.5m each to vote for Qatar.

In a lengthy and at times furious statement running to four pages the officials called the claims "distressing, insulting and incomprehensible". The statement cast doubt on the "credibility of the reporters, their motivations and extent to which ... the evidence in any way can be relied upon".

Monday night's BBC Panorama contained further revelations, accusing Fifa of trying to block the names of two senior figures in world football who were forced by Swiss prosecutors to repay bribes from the sports marketing company ISL in the 1990s. A programme broadcast on the eve of the World Cup vote in December last year had accused Leoz, Teixeira and the Cameroonian Issa Hayatou of being on a list of 175 payments totalling $100m made by ISL. All three denied the allegations.

Blatter, whose lead over Bin Hammam appears increasingly unassailable, on Monday continued his strategy of promising to rebuild Fifa's reputation while also defending its integrity. "We shall find a solution how to handle the past ... in order that we can stop forever in the future all these damaging things about corruption," Blatter said. "We have to make sure that in the next term of office immediately starting after the election that we rebuild the image of Fifa," said the 75-year-old Swiss, who joined Fifa in 1975.

Blatter discussed a bribe he was offered during the period when he acted as Fifa's secretary general under the former president João Havelange. "In this envelope there was an amount of money. I couldn't refuse because he put it in my pocket," said Blatter, declining to identify who made the offer. "I came home here to Fifa and gave it to the finance director and he put this money on the account of the Swiss Bank Corporation."

The cash, which Blatter has said amounted to 50,000 Swiss francs, was later withdrawn by the person who gave him it, Blatter said, adding: "Then it was specifically known that please don't try to give money to somebody who's in the Fifa."